Final answer:
Without the specific coordinates of the purple point in question, we cannot choose a set of vertex points that define a quadrilateral ABCD as a square that includes the purple point inside.
Step-by-step explanation:
The question asks for the vertex points that would define a quadrilateral ABCD to be square and encompass a purple point within its boundaries. Given a choice of four different sets of vertex points, we need to determine which one represents a perfect square and includes the interior point.
To ensure that we have a square, we must look for four points that create equal sides and have right angles at each corner. Looking at the options:
A. (0,0), (2,0), (2,2), (0,2) - This forms a square with sides of length 2 units.
B. (1,1), (2,1), (2,2), (1,2) - This also forms a square but with sides of length 1 unit.
C. (0,0), (1,0), (1,1), (0,1) - This forms a square with sides of length 1 unit.
D. (0,0), (3,0), (3,3), (0,3) - This forms a square with sides of length 3 units.
If the purple point is at (5,5) as given in the unrelated reference information, we need a square large enough to contain this point. Option D, with vertex points at the origin and extending to 3 units in both x and y directions, would be the only square that can contain a point at (5,5). However, since no context is provided about the actual location of the purple point in the student's question, we cannot conclusively choose an option without that specific information.